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. 2018 Jul 2;8:9910. doi: 10.1038/s41598-018-28236-w

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Localization of the eigenmodes. The distribution P(Y_Q) of the community participation ratio Y_Q of a single realization of N = 6400 nodes of a CNM is shown for D = 1 (panel a), D = 2 (panel b) and D = 3 (panel c). The total number of communities in these networks are: 30 (panel a), 18 (panel b) and 12 panel (c). Observe that Y can be larger in lower dimensions; this is because the modularity is smaller in lower dimensions and the community-detection algorithm divides the network in more communities.